17.2.1999/H. Väliaho
Pronunciation of mathematical expressions
The pronunciations of the most common mathematical expressions are given in the list
below. In general, the shortest versions are preferred (unless greater precision is necessary).
1. Logic
∃
there exists
p⇒q
p implies q / if p, then q
∀
p⇔q
for all
p if and only if q /p is equivalent to q / p and q are equivalent
2. Sets
x∈A
x belongs to A / x is an element (or a member) of A
x∈
/A
x does not belong to A / x is not an element (or a member) of A
A⊃B
A contains B / B is a subset of A
A⊂B
A is contained in B / A is a subset of B
A∩B
A cap B / A meet B / A intersection B
A\B
A minus B / the difference between A and B
A∪B
A cup B / A join B / A union B
A×B
A cross B / the cartesian product of A and B
3. Real numbers
x+1
x plus one
x−1
x minus one
x±1
x plus or minus one
xy
xy / x multiplied by y
(x − y)(x + y)
x
y
x minus y, x plus y
=
the equals sign
x=5
x equals 5 / x is equal to 5
x 6= 5
x (is) not equal to 5
x over y
1
x≡y
x is equivalent to (or identical with) y
x 6≡ y
x is not equivalent to (or identical with) y
x>y
x is greater than y
x≥y
x is greater than or equal to y
x<y
x is less than y
x≤y
x is less than or equal to y
0<x<1
zero is less than x is less than 1
0≤x≤1
zero is less than or equal to x is less than or equal to 1
|x|
mod x / modulus x
x3
x cubed
x4
x to the fourth / x to the power four
xn
x to the nth / x to the power n
x−n
√
x
√
3
x
√
4
x
√
n
x
x to the (power) minus n
x
2
x squared / x (raised) to the power 2
(x + y)
³ x ´2
y
(square) root x / the square root of x
cube root (of) x
fourth root (of) x
nth root (of) x
2
x plus y all squared
x over y all squared
n!
n factorial
x̂
x hat
x̄
x bar
x̃
x tilde
xi
xi / x subscript i / x suffix i / x sub i
n
X
ai
the sum from i equals one to n ai / the sum as i runs from 1 to n of the ai
i=1
4. Linear algebra
kxk
−−→
OA
the norm (or modulus) of x
OA
OA / the length of the segment OA
AT
A transpose / the transpose of A
A−1
A inverse / the inverse of A
OA / vector OA
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5. Functions
f (x)
f x / f of x / the function f of x
f :S→T
a function f from S to T
x 7→ y
x maps to y / x is sent (or mapped) to y
f 0 (x)
f prime x / f dash x / the (first) derivative of f with respect to x
f 00 (x)
f double–prime x / f double–dash x / the second derivative of f with
respect to x
f 000 (x)
f triple–prime x / f triple–dash x / the third derivative of f with respect
to x
f (4) (x)
f four x / the fourth derivative of f with respect to x
∂f
∂x1
the partial (derivative) of f with respect to x1
∂2f
∂x21
Z ∞
the second partial (derivative) of f with respect to x1
the integral from zero to infinity
0
lim
x→0
the limit as x approaches zero
lim
the limit as x approaches zero from above
lim
the limit as x approaches zero from below
x→+0
x→−0
loge y
log y to the base e / log to the base e of y / natural log (of) y
ln y
log y to the base e / log to the base e of y / natural log (of) y
Individual mathematicians often have their own way of pronouncing mathematical expressions and in many cases there is no generally accepted “correct” pronunciation.
Distinctions made in writing are often not made explicit in speech; thus the sounds f x may
−−→
be interpreted as any of: f x, f (x), fx , F X, F X, F X . The difference is usually made clear
by the context; it is only when confusion may occur, or where he/she wishes to emphasise
the point, that the mathematician will use the longer forms: f multiplied by x, the function
f of x, f subscript x, line F X, the length of the segment F X, vector F X.
Similarly, a mathematician is unlikely to make any distinction in speech (except sometimes
a difference in intonation or length of pauses) between pairs such as the following:
x + (y + z) and (x + y) + z
√
√
ax + b and
ax + b
an − 1
and an−1
The primary reference has been David Hall with Tim Bowyer, Nucleus, English for Science
and Technology, Mathematics, Longman 1980. Glen Anderson and Matti Vuorinen have
given good comments and supplements.
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Université Louis Pasteur - Strasbourg I
UFR Maths-Info
Anglais Scientifique 2006-2007
Licence
Reading Mathematical Expressions
(A. Oancea, S. Maillot, C. Mitschi)
Note: Some groups of letters are underlined in order to draw one’s attention to their pronunciation.
Basics
a+b
a−b
a·b
a
, a/b
b
1 1 1
1
, , , ...,
2 3 4
10
5 2
7
, , ...,
2 3
10
a=b
a = b
a<b
a≤b
a>b
a≥b
a plus b
a minus b
ab, a times b
a over b, a divided by b
one half, one third, one fourth, ... , one tenth
five halves, two thirds, ... , seven tenths
a
a
a
a
a
a
equals b, a is equal to b
different from b, a not equal to b
(strictly) less than b
less than or equal to b
(strictly) bigger than b, a greater than b
greater than or equal to b
Powers and roots
ab
a to the b,
a to the b-th (power) [if b is a positive integer]
2
x
x squared
x3
x cubed
−1
x√
x inverse
n
√ t n-th root of t
t square root of t
√
3
t cubic root of t
1
Sets
∅
A∪B
A∩B
Ac
A\B
A×B
x∈A
(the) empty set
A union B
A intersected with B
the complement of A
A minus B
A times B
x in A, x belongs to A, x belonging to A
Miscellaneous
5%
30◦
xk
j
x
i n
2
k=1 k
n
2k+1
k=1 2k+2
n!
partie entière de x
|x|
|z|
Re(z), Im(z)
x
v, w
cos sin tan etc.
ηθξ
πσχψ
R2 , R3 , Rn
(blablabla) · (blbl)
blablabla
blbl
x 1 , . . . , xn
five percent
thirty degrees
xk
x i j [if j is an index, not an exponent!]
sum k equals 1 to n of k 2 ,
sum for k (running) from 1 to n of k 2 ,
summation k from 1 to n of k 2
product k equals 1 to n
of 2k + 1 over 2k + 2
product for k (running) from 1 to n
of 2k + 1 over 2k + 2
n factorial
integer part of x
absolute value of x (if x is a real number)
modulus of z (if z is a complex number)
real part of z, imaginary part of z
norm of x
scalar product of v and w
cosine/cosinus sine/sinus tangent etc.
eta [ı́ta] theta [thı́ta] xi [ksái]
pi [pái] sigma [zı́gma] chi [kái] psi [sái]
R 2, R 3, R n
blablabla, the whole times blbl
blablabla, the whole divided by blbl
x1 up to xn
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Calculus
f
f prime, f dashed
d by dx
df by dx
d x f , partial derivative of f with respect to x
d
dx
df
, ∂f
dx ∂x
∂ f
x b
f (s)ds
a ,
D
±∞
lim f (x)
integral from a to b (of) f (s) ds
double integral, triple integral over the domain D
D
x→a
log(x), loga x
exp(x), ex
plus/minus infinity
(the) limit of f (x) as x tends/goes to a,
(the) limit of f of x as x tends/goes to a
logarithm of x, logarithm in base a of x
exponential of x, e to the x
Functions
f :U →V
f (x)
x → f (x)
of class C k
of class C ∞
the Lebesgue spaces Lp , L∞
the Sobolev spaces H k , W k,p
f from U to V
f of x
x maps to f (x)
of class C k
of class C infinity
the Lebesgue spaces L p, L infinity
the Sóbolev spaces H k, W k p
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